Hello!

Background checks are nothing to be worried about, as long as you haven´t lied (e.g., saying that you graduated from Uni X when you didn´t, or that you worked in Company Y 2 years instead of 6 months). Minor things, such as 1 month differences, etc. don´t matter. 

Most of the times, they are done by 3rd party companies to which the job is externalized. If they find any discrepancy, they contact you first and clarify it with you. 

For instance, with the MIT background check I had the issue that the external name of my Amazon job is not the same as the one Amazon uses internally -and that was the name given in the certificated that Amazon gives oficially-. It was easily solved by an HR doc that explained that both were the same thing. 

Hope it helps!

Cheers, 

Clara

They will confirm were you studied and possibly your grade. 

They won't check your %, particularly as the university does not provide this - and for sure they won't have a way to find how many contenders were there. They won't probably even check if you were actually the VP of that student organization.